To find the equation of line parallel to Ax+By+C=0, we use the fact that parallel lines have the same slope. This is a fundamental concept in coordinate geometry and is often asked in exams. AkLearningNepal
Given Line
Equation of the given line is:
Ax + By + C = 0
Slope of Given Line
Rewrite in slope form (y = mx + k):
By = −Ax − C
y = (−A/B)x − (C/B)
So, slope (m) = −A/B.
Equation of Parallel Line
Any line parallel to the given line must have the same slope −A/B.
So its general form is:
y = (−A/B)x + k
Multiply by B:
B y = −A x + Bk
Rearranging, we get:
Ax + By + D = 0
where D = Bk is a new constant.
Note:
All lines parallel to Ax + By + C = 0 are of the form Ax + By + D = 0, where D ≠ C.
Equation of Any Line Parallel to Ax + By + C = 0
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